What's the most lightweight format for textures?
The GPU does not work in terms of jpeg, png, tiff, tga, etc. During rendering every image that is used as a texture has to be stored in vram using a format that is determined by the engine, so in this case Eevee. This can range from uncompressed to various hlsl/glsl/cuda friendly compressed variants. You cannot really influence that format unless Eevee exposes its internal texture format as a config option.

The source image format you use for your textures will be converted to that internal format once, not on every frame, unless you change your source texture every frame via script or something.